Let Y, represent the ith normal population with unknown mean , and unknown variance of for i=1,2. Consider independent random samples, Ya, Ya, Yin, of size n,, from the ith population with sample mean Y, and sample variance S7=E(-)². (h) Find the standard error of U₂ in part (g), assuming that of = 0} = 0². (i) Discuss how the distribution of Y₁ - ₂ can be used to test the equality of the two population means, 41 and 42, when o=o=o² is known. (i) Define appropriate rejection regions, in terms of Y₁-Y2, for testing Ho: ₁ = 2 against a two-sided alternative hypothesis at the a level of significance.

Q: 15

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